Reid’s measure calls for higher taxes on people earning $1 million or more in a year.
Republicans helped push the resolution over an initial 60-vote hurdle on Thursday in a 74-22 vote, but GOP support for the resolution is far from certain in Monday's vote which requires the same threshold.
If the resolution were to clear Monday's vote, it would face one final vote that would require a simple majority.
Reid put forward the proposal on Tuesday as a way to meet Republican demands to begin considering bills related to the debt ceiling and budget deficit crises. If passed, the resolution would express only the "sense of the Senate" and not carry the force of law.
Since Reid offered the resolution it has become a favorite punching bag for Republicans who have derided it as a waste of the Senate's time.
Sen. Orrin HatchOrrin HatchOvernight Tech: Dem wants to see FCC chief's net neutrality plans | New agency panel on telecom diversity | Trump calls NASA astronaut Lighthizer expected to win committee approval to lead trade office Overnight Finance: Trump wants 15 percent corporate rate | GOP tax team huddles with Trump aides | Shutdown watch over border wall MORE (R-Utah), for example, roasted Democratic leadership over the resolution on Wednesday, claiming it was a cheap stunt.
“The leadership in the Senate offered a nonbinding resolution designed solely to score some cheap political points that will jazz up the activist left to demagogic class warfare against individuals with high incomes,” Hatch warned. “I guarantee you, if we raise taxes, my friends on the other side will spend every dime of it.”